diff --git a/sympy/assumptions/handlers/ntheory.py b/sympy/assumptions/handlers/ntheory.py
index 4f1397b283..006f1d2cdd 100644
--- a/sympy/assumptions/handlers/ntheory.py
+++ b/sympy/assumptions/handlers/ntheory.py
@@ -127,6 +127,12 @@ def _EvenPredicate_number(expr, assumptions):
         return False
     if isinstance(expr, (float, Float)):
         return False
+    # Check if the expression is a division of a power by 2
+    if isinstance(expr, Mul) and len(expr.args) == 2:
+        pow_expr, div_by_two = expr.args
+        if isinstance(div_by_two, Rational) and div_by_two == Rational(1, 2):
+            if isinstance(pow_expr, Pow) and ask(Q.even(pow_expr.base), assumptions) and pow_expr.exp == 2:
+                return True
     return i % 2 == 0
 
 @EvenPredicate.register(Expr)
